Answer:
<u>Jax</u> will pay for (his) lunch with cash today.
Explanation:
"His" is not a pronoun. It is a possessive adjective: my, your, his, her, its, our, your, their. It is called so because it precedes a noun and modifies it. Therefore, if you say "his" lunch, it is not about any lunch; it is rather a specific one, belonging to a particular person.
The antecedent of "his" is "Jax", since "his lunch" refers to "Jax's lunch", that is, Jax is the person whose lunch we are talking about.
Each of the conference rooms has a computer display.
